Lcr Circuit

Key Idea In resonance condition, maximum current flows in the circuit Current in LCR series circuit,

i%3D%5Cfrac%7BV%7D%7B%5Csqrt%7B%7B%7BR%7D%5E%7B2%7D%7D%2B%7B%7B(%7B%7BX%7D_%7BL%7D%7D-%7B%7BX%7D_%7BC%7D%7D)%7D%5E%7B2%7D%7D%7D%7D

where V is rms value of current, R is resistance,

%7B%7BX%7D_%7BL%7D%7D

is inductive reactance and

%7B%7BX%7D_%7BC%7D%7D

is capacitive reactance. For current to be maximum, denominator should be minimum which can be done, if

%7B%7BX%7D_%7BL%7D%7D%3D%7B%7BX%7D_%7BC%7D%7D

This happens in resonance state of the circuit ie,

%5Comega%20L%3D%5Cfrac%7B1%7D%7B%5Comega%20C%7D

L%3D%5Cfrac%7B1%7D%7B%7B%7B%5Comega%20%7D%5E%7B2%7D%7DC%7D

..(i) Given,

%5Comega%20%3D1000%5C%2C%7B%7BS%7D%5E%7B-1%7D%7D%2CC%3D10%5C%2C%5Cmu%20F%3D10%5Ctimes%20%7B%7B10%7D%5E%7B-6%7D%7D%5C%2CF

Hence,

L%3D%5Cfrac%7B1%7D%7B%7B%7B(1000)%7D%5E%7B2%7D%7D%5Ctimes%2010%5Ctimes%20%7B%7B10%7D%5E%7B-6%7D%7D%7D

%3D0.1%5C%2CH

%3D100%5C%2CmH

Chapter Questions
1 MCQs